# Have PCs Solve The Three Body Problem? **URL:** \ **Category:** Factual Questions\ **Created:** [August 11, 2003, 2:02am UTC](https://boards.straightdope.com/t/have-pcs-solve-the-three-body-problem/194298 "2003-08-11T02:02:00Z")\ **Posts on this page:** 6\ **Page:** 1
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [August 11, 2003, 2:02am UTC](https://boards.straightdope.com/t/have-pcs-solve-the-three-body-problem/194298/1 "2003-08-11T02:02:00Z")
Maybe I’ve been asleep, but can computers (from PCs to Super Computers) solve the three body problem? Or, do they simply help us to make more accurate approximations? If computers cannot solve it, is it because our best algorithms are limited by our mortal capabilities? (In other words, is the model we use simply limited by the abilities of those who built the model?) - Jinx ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [August 11, 2003, 2:19am UTC](https://boards.straightdope.com/t/have-pcs-solve-the-three-body-problem/194298/2 "2003-08-11T02:19:25Z")
Three-body problems usually have no _analytical_ solutions, i.e. something you can write out as a formula. But it’s possible to calculate a _numerical_ solution (i.e. a table of values instead of a formula) to an arbitrary precision. ---
**Author:** ![Atlantis](https://avatars.discourse-cdn.com/v4/letter/a/9de0a6/32.png) [@Atlantis](https://boards.straightdope.com/u/Atlantis)\ **Post date:** [August 11, 2003, 2:38am UTC](https://boards.straightdope.com/t/have-pcs-solve-the-three-body-problem/194298/3 "2003-08-11T02:38:50Z")
Out of curiosity, what’s the Three Body Problem? ---
**Author:** ![jmizzou](https://avatars.discourse-cdn.com/v4/letter/j/edb3f5/32.png) [@jmizzou](https://boards.straightdope.com/u/jmizzou)\ **Post date:** [August 11, 2003, 3:14am UTC](https://boards.straightdope.com/t/have-pcs-solve-the-three-body-problem/194298/4 "2003-08-11T03:14:42Z")
From [http://scienceworld.wolfram.com/physics/Three-BodyProblem.html:](http://scienceworld.wolfram.com/physics/Three-BodyProblem.html:) > [@](#): > > The problem of computing the mutual gravitational interaction of three masses. This problem is surprisingly difficult to solve, even in the so called restricted three-body problem, corresponding to the simple case of the three masses moving in a common plane. ---
**Author:** ![Popup](https://avatars.discourse-cdn.com/v4/letter/p/94ad74/32.png) [@Popup](https://boards.straightdope.com/u/Popup)\ **Post date:** [August 11, 2003, 8:08am UTC](https://boards.straightdope.com/t/have-pcs-solve-the-three-body-problem/194298/5 "2003-08-11T08:08:37Z")
> [@](#): > > \*Originally posted by Atlantis \* > \*\*Out of curiosity, what’s the Three Body Problem? \*\* In Newtonian (classical) physocs, every body with a mass attracts every other body (with a mass) with a force that depends only on their weights and the distance (F = G m[sub]1[/sub] m[sub]2[/sub] / R[sup]2[/sup]). If you have two bodies, it’s farily straightforward to calculate these forces, and the effect they will have on the trajectories of the two bodies. (They will most likelly end up in elliptical orbit around their center of gravity.) For three bodies, however, it gets tricky. It’s still fairly easy to calculate the forces at any given time, but to predict the trajectories gets really hairy. There is no (known) analytical expression to predict the position of the three bodies at an arbitrary future time. It is, of course, possible to calculate numerically with an arbitrary precision, by calculating the forces at time T[sub]1[/sub], use this to predict where they will be at time T[sub]1[/sub]+epsilon, etc. I believe that the OP wanted to know if there had been any advances along those lines, but as far as I know there haven’t been any. (Does anyone know if it has been **proved** that there’s no analytical solution to the three-body problem?) [joke] In Aristotelian physics, everything was deterministic and well-defined. In Newtonian physics, we can’t solve the three-body problem. In Einsteinian physics, we can’t solve the two-body problem. In Heisenbergian physics, we can’t even know where one particle is. In Quantum Electrodynamics, we can’t even solve the equation for vacuum. [/joke] ---
**Author:** ![raygirvan](https://avatars.discourse-cdn.com/v4/letter/r/ac91a4/32.png) [@raygirvan](https://boards.straightdope.com/u/raygirvan)\ **Post date:** [August 11, 2003, 10:12am UTC](https://boards.straightdope.com/t/have-pcs-solve-the-three-body-problem/194298/6 "2003-08-11T10:12:32Z")
Further problem: many cases in the Three Body Problem give [chaotic solutions](http://www.physics.drexel.edu/~steve/triple.html) - sensitivity to vanishingly small differences in initial conditions - so even higher numerical precision won’t help.